 # JavaScript Math atanh()

In this tutorial, you will learn about the JavaScript Math.atanh() method with the help of examples.

The `atanh()` method computes the hyperbolic arctangent of the specified value and returns it.

### Example

``````// hyperbolic arctangent of 0.75
let number = Math.atanh(0.75);
console.log(number);

// Output: 0.9729550745276566``````

## atanh() Syntax

The syntax of the `Math.atanh()` method is:

``Math.atanh(number)``

Here, `atanh()` is a static method. Hence, we are accessing the method using the class name, `Math`.

## atanh() Parameter

The `atanh()` method takes a single parameter:

• `number` - between -1 and 1 whose hyperbolic arctangent is to be calculated

## Math.atanh() Return Value

The `atanh()` method returns:

• hyperbolic arctangent of the argument `number`
• NaN (Not a Number) if the argument is either non-numeric or greater than 1 or less than -1

## Example 1: JavaScript Math.atanh() with argument between -1 and 1

``````// hyperbolic arctangent of 0
let number1 = Math.atanh(0);
console.log(number1);

// hyperbolic arctangent of 0.5
let number2 = Math.atanh(0.5);
console.log(number2);

// Output:
// 0
// 0.5493061443340548``````

In the above example,

• `Math.atanh(0)` - computes the hyperbolic arctangent of 0
• `Math.atanh(0.5)` - computes the hyperbolic arctangent of 0.5

Note: Hyperbolic arctangent i.e, `atanh(number)` is a unique number 'x' in the range [-1, 1] such that `tanh(x)` = `number`.

## Example 2: Math.atanh() for Argument not in the Range -1 to 1

``````// argument greater than 1
let number1 = Math.atanh(2);
console.log(number1);

// argument less than -1
let number2 = Math.atanh(-4);
console.log(number2);

// Output:
// NaN
// NaN``````

The `atanh()` method returns NaN because both the arguments 2 and -4 are not in the range -1 and 1.

## Example 3: Math.atanh() for Arguments -1 and 1

``````// atanh() with argument -1
let number1 = Math.atanh(-1);
console.log(number1);

// atanh() with argument 1
let number2 = Math.atanh(1);
console.log(number2);

// Output:
// -Infinity
// Infinity``````

The `atanh()` method returns:

• Infinity - if the argument is 1
• -Infinity - if the argument is -1

## Example 4: Math.atanh() with Non-Numeric Arguments

``````let string = "Harry";

// atanh() with string argument
let value = Math.atanh(string);
console.log(value);

// Output: NaN``````

In the above example, we have tried to calculate the hyperbolic arctangent of the string `"Harry"`. Hence, we get NaN as the output.